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“That’s not art!” is a not uncommon reaction to Marcel Duchamp’s Fountain. As we ponder the mounted urinal with letters scrawled across it, the question equally arises, “if it isn’t art, why isn’t it art?” And this must naturally lead to the fundamental question, “what is art anyway?” This confusion that comes to the average person when encountering certain “modern art” is further confused by the general ambiguity and broad use of the term “art” in a variety of contexts. For we sometimes speak of the “medical arts,” the “performing arts,” the “liberal arts,” “the culinary arts,” or we may even speak of the “art of basketball,” or the “art of living well.” So, what exactly is “art” and how do we know if something like Fountain would constitute a work of art?

The purpose of this essay is neither to offer an evaluation of whether Fountain is “art” nor whether if it is art, whether it is good or bad. Rather, this essay seeks to outline a beginning taxonomy through which we could possibly consider these questions. A single definition of “art” seems unlikely to account fully for the variety of objects and activities that we normally speak of as “arts.” For this reason, classifying different kinds of “arts” might possibly help us to understand the variety of ways we experience art in the world.

The first major division of “art” is the somewhat self-referential distinction of art as a “cause” on the one hand, and as an “effect” on the other. When we speak of art as a “cause,” it refers to the rules that govern an action and the skills needed to achieve some end; thus we speak of the “art of basket-weaving” or the “art of ship-building,” etc. Art as an “effect,” refers to the “work of art” that is produced as a result of the actions of the one operating under the rules and skills of production. So the cause of the basket is the “art of basket weaving,” and the effect of basket-weaving is the “basket” which is produced. Both these (cause and effect) are properly “arts.”

We can refer to that which is produced as an “artifact,” but not all “arts” (as a cause) produce artifacts (as an effect). For example, the “medical arts” (as a cause) refers to all the scientific knowledge concerning the health of the body, along with the various skills needed to attain that health (like surgery or diagnosis). However, the one practicing the “medical arts” does not produce an “artifact.” Instead, the “health of the body” is the effect of the causal “medical arts.” Similarly, the “art of logic” (cause) produces syllogisms (effect), and the “art of governing” (cause) leads to the “act of ruling” (effect), but neither produce artifacts.

The two notions of art, however, are not on equal footing logically. For “art as cause” is the fundamental meaning of “art;” while “art as effect” is derivative or dependent (as is the case with all cause and effect relationships). Aristotle, Thomas Aquinas, and Kant all seem to agree on this point. Aristotle defines “art” as “identical with a state of capacity to make, involving a true course of reasoning” (Aristotle, Nicomachean Ethics, 1140a9-10). And likewise says Thomas, “Art is nothing else but the right reason about certain works to be made. . . . Art, properly speaking, is an operative habit” (Thomas, Summa Theologica, I-II. Q. 57 A. 3). The cause is fundamental because it must come prior to the effect—without knowledge of “how-to” there can be nothing produced.

On this account, all actions have an “art”—it is the “know-how” to produce a desired effect, and all “arts as effects” will have a corresponding series of rules governing their production. (This statement is not entirely accurate, as will be seen below. For, according to Kant, the distinguishing characteristic of the “fine arts” is precisely the lack of universal governing rules, and yet there being an effect desired by the work of the artist. How these two ideas can work together consistently will be explored below.) Hence Thomas’ reference to art as “right reason” concerning things “to be made”. And so points out Kant that “every art presupposes rules which are laid down as the foundation which first enables a product, if it is to be called one of art, to be represented as possible” (Kant, Critique of Judgement, 136.).

Art, therefore, is like science in that it involves a kind of speculative knowledge concerning the nature of reality. However, “science,” properly speaking, aims at knowledge of “what is,” while “art” aims at knowledge of “how to make X” or how to achieve a desired effect. In some cases there is clear overlap between “science” and “art”—as is the case of the “science of medicine” and the “art of medicine.” For without the “science of medicine” it is dubious that a doctor could achieve the health of the body, which is the desired effect of the “art of medicine.” On the other hand, some arts seem to be able to operate somewhat independently of the corresponding science. For example, it seems that a person can be quite capable in the “musical arts” yet have little knowledge “music theory”—and vice-versa.

The remaining discussions of the various kinds of “art” all deal with arts as “effects.” In the first major sub-division of “art as effect” we can distinguish between arts which produce something outside of the artist and arts which work on the mind of the artist (i.e., those which do not produce something outside the artist). The latter of these are called “liberal arts” and are most closely associated with education. According to Mortimer J. Adler, “the liberal arts are traditionally intended to develop the faculties of the human mind, those powers of intelligence and imagination without which no intellectual work can be accomplished…once all were acquired, the student was “free” to stand before all things as a whole, both to know and to act” (Adler, What Is Liberal Education?). Traditionally the liberal arts were seven in number, constituting the language and mathematics arts necessary for the student to be “free” to know and to act in the world.

The former arts (those which produce something outside the artist) are variously called the “mechanical arts,” the “servile arts,” or the “practical arts.” What they have all in common is some end beyond the formation of the human mind. For example, the “medical arts” would fall under this category because the end of the art is something produced outside of the doctor (i.e., the health of the body of the patient). Hence, in this category would fall all manner of “arts” which will need to be further divided—for within this category of arts would include such things as the “art of carpentry,” the “art of the pianist,” the “medical arts,” and even the “fine arts.”

In further separating the “arts” at this point, Immanuel Kant is most instructive. According to Kant, when it comes to arts which produce something outside the artist, there are two broad categories: the “mechanical arts” and the “aesthetic arts.” The difference between the two are the ends the artist has in mind when creating the artwork. To understand the difference, we must go back the original distinction between “art as cause” and “art as effect.” There it was argued that all “art” is created according to the “universal reason”—that is according to some rule. These “arts” are here called the “mechanical arts”—they are arts made for some use. And hence they are sometimes called the “useful arts.” Here would include certain “industrial arts” like carpentry, ship-building, etc.

However, according to Kant, the “aesthetic arts” have no “useful” purpose in mind when they are created, or rather, they are not created according to a “universal rule”. The consequence of this, is that there is no “right or wrong” to the “aesthetic arts” in the same way there is a “right or wrong” in the production of a chair. For the chair, there are universal rules of carpentry by which the artisan works, but not so the painting. There is no “right or wrong” way to paint the Flint Hills. Furthermore, the painting of the Flint Hills is not made for some use in the same way that the chair is made for sitting.

“Aesthetics arts,” however, are not without an end, for the artist must have some end in mind when acting, otherwise he would not act. According to Kant, the end of these arts is pleasure. As such, Kant distinguishes between two kinds of “aesthetic arts:” “agreeable arts” and “fine arts.” The “agreeable arts” have pleasure as “sensation” as their end. Here Kant seems to have in mind perhaps the “culinary arts” and such “arts” as are pure enjoyment, as in “entertaining narrative, the art of engaging the whole [dinner] table in unrestrained and sprightly conversation, or with jest and laughter inducing a certain air of gaiety” (Kant, Critique of Judgement, 134-135).

And so we have finally arrived at the distinguishing features of the “fine arts.” The “fine arts” belong to that broad category of arts which are effects of human actions and which produce something outside of the one acting, and yet are ones for which there is no use. But unlike the “agreeable arts,” the “fine arts” are presented not as objects of “sensational enjoyment” but of a pleasure aimed at “modes of cognition.” That is, they are presented as objects of Beauty. Kant seems to have in mind Thomas Aquinas’ understanding of Beauty: “Beauty,” says Thomas, “relates to the cognitive faculty; for beautiful things are those which please when seen” (Thomas, Summa Theologica, I. Q. 5 A. 4). And by “seen” Thomas and Kant have in mind “seen by the mind.” So, if we ask the question, “what is that painting for?” the answer is “for enjoyment, for contemplation.”

Kant also denies that “fine arts” are meant to communicate something. Because “fine arts” are not made according to a universal rule, and although they present Beauty to the mind for contemplation, the “fine arts” are devoid of concepts. That is, they are not meant to “mean” one thing or another. Says Kant, the “fine arts” do not “permit of the judgement upon the beauty of its product being derived from any rule that has a concept for its determining ground” (Kant, Critique of Judgement, 136). So to ask, “what does this painting ‘mean’?” is to misunderstand the “fine arts.” “Fine arts” are presented to the mind as an object of Beauty for contemplation, which is what Thomas indicates is the nature of “beautiful things.”

One final division of “arts” should be addressed. Within the “fine arts” we can distinguish between “plastic arts” and “performing arts.” Both of these would contain the characteristics described for “fine arts” above. The difference here is that “plastic arts” would constitute whole, or completed art forms which involve the manipulation of matter. Such things as painting, sculpting, ceramics, etc. would fall into this category of “fine arts.” The “performing arts,” by contrast, are “fine arts” which are always “in progress” in their presentation. Such art forms as theatre or “musical arts” would fall into this category. A musical performance, by its nature, is always in “progress” of presentation, unlike a sculpture which is a completed whole.

If we now return to our original queries concerning Duchamp’s Fountain, we now have the conceptual categories with which to place it. The original urinal that Duchamp repurposed would seem to fall under that category of industrial arts which produce ceramic fixtures. The fixtures are made for certain uses according to universal rules. The question, however, whether something can be repurposed and presented as “fine art” by merely scrawling some letters on an object and calling it “fine art” is not something we are capable of evaluating at this point. The general direction of the discussion would seem to allow for such a piece as constituting “fine art.” If it is a “fine art” we are still left with the question of whether it is any good. Kant would seem to indicate that that question itself violates the nature of the “fine arts” and Beauty. What we have not explored in this essay is the true nature of Beauty and whether it has an objective definition. Thomas indicates it does, Kant that it does not. The method by which we could evaluate Fountain would have to settle this definition first, for the “fine arts” depends upon presentation of “art” as an object of Beauty for contemplation. If Beauty does have objective content we could possibly evaluate Fountain as either “good” or “bad,” but if Beauty has no objective content the most we could say is that we either find Fountain “enjoyable” or “unenjoyable” as a judgment of the mind. What we have seen, nevertheless, is that Fountain falls generally within the definition of “fine arts,” and what we mean by the “fine arts.” So, yes, that’s art!

In a survey of books used for education throughout the history of Western civilization two books stand out: the Bible and Euclid’s Elements (Carl B. Boyer and Uta C. Merzbach, A History of Mathematics, 119). Poet and schoolmaster Edna St. Vincent Millay says of the Elements that “Euclid alone has looked on Beauty bare.” And Euclid earned a spot amongst Raphael’s School of Athens painting alongside Plato and Aristotle. What can account for such high praise and popularity? Is it that Euclid has laid the foundations for all mathematics? If so, why has Euclid been left behind in the modern classroom? Is there any value in a return to Euclid? What value might there be in studying Euclid today?

It may be too strong a claim to say that the Elements provide the foundation for all mathematics. Nevertheless, the basic principles or axioms of many of the branches of mathematics can, in fact, be seen in Euclid. In the classical mathematical Quadrivium of Arithmetic, Geometry, Music, and Astronomy, we see that Geometry is but one of the fundamental subjects of mathematics. Yet, in Euclid’s Elements there are applications and axioms for the other branches. For example, his earliest axioms like, “If equals be added to equals, the wholes are equal” have clear implications for the axioms (if not being identical) in Arithmetic. The proofs for relationships of ratios throughout Book X (and elsewhere) have clear implications for the science of Music which deal in harmonies and patterns. And certainly the principles of trigonometry that are laid down by Euclid have far reaching application from Astronomy to sea-faring to engineering.

Yet Euclid does not specifically set forth the axioms of those other branches. However, to the student who is attentive, the Elements does teach an important principle concerning the nature of learning and of certain disciplines. In demonstrative sciences one always begins with axioms and definitions and then begins to reason from those assumptions. They are the grounds or conditions of the reasoning that follows. In this sense they are indemonstrable. To ask for such demonstrations is to misunderstand the nature of the science. For example, Aristotle in the Metaphysics, sets forth to show that the Principle of Non-Contradiction (the foundations of Logic itself) cannot and should not be demonstrated. To attempt a proof is to misunderstand the nature of proof, for one cannot prove it without assuming it. The best Aristotle can do in this case is show that it is impossible to deny, because to deny it, one must assume it. In Geometry it would be improper for Euclid to attempt to prove that “a proportion in three terms is the least possible.” Rather, this definition functions as an assumption from which the proofs proceed.

As indicated from the example from Aristotle, Geometry is not the only science that proceeds in this fashion. The student who is attentive in his studies of the Elements should see parallels in other disciplines as well, such as the philosophical and theological sciences. Just as there are axioms of Geometry, so too are there axioms of philosophy and theology that are not subject to proof, but are the grounds from which reasoning proceeds. This may be one of the mistakes of Descartes in Epistemology: he attempted to assume nothing and prove everything. A task which is impossible, for all disciplines requires axioms. Even Moral Philosophy, of which Thomas Aquinas asserts the axiom of all action is: “good is to be done and pursued, and evil is to be avoided” (Summa Theologica, II-I, Q. 92, A. 1).

This may partially account for the staying-power of the Elements throughout history, the implicit lesson about the nature and procedure of demonstrative sciences. In addition to this, the one who studies Euclid does not just study Geometry. For the Elements is also a lesson in the Trivium of Grammar, Logic, and Rhetoric. That is, Euclid bridges the gap between the Trivium and the Quadrivium. This is also why Euclid may appeal to those persons who find mathematics difficult or intimidating. For as a modern student peruses the Elements they may be struck with how “unmathematical” it appears. There are no numbers, no Cartesian coordinate planes, no formulas. It is as much a book of literature as it is of geometry. This may account for the testimony throughout history of its elegance and beauty. For each of Euclid’s proofs begin with an assertion followed by the elegant “for if not” reductio ad absurdum and ending with pointed “the very thing which was to be shown” (Q.E.D.) or “the very thing which was to be done” (Q.E.F.). Thus, in the process of learning Geometry, the student also learns Grammar and Logic, as well as certain principles of persuasive argumentation (Rhetoric). This may also account for the popularity of the Elements in education.

Will Euclid ever be used again to the same degree as he was in the past? This seems unlikely for a number of reasons. First, there is a need for certain modern concepts in geometry like the Cartesian coordinate plane. Second, textbook companies have no incentive in publishing Euclid since the Elements is in the public domain. Third, the modern student (for a variety of reasons beyond the scope of this essay) may no longer have the capability to read Euclid as an introductory text on Geometry. Yet, for the student who struggles with mathematics, Euclid may be a way to bridge the gap between the humanities and mathematics. And maybe, these students too may come to see that: “Euclid alone has looked on Beauty bare.”

As we look over the plethora of options for education available to us, how we to decide what education is best? There is “on the job training,” vocational schools, technical schools, nursing schools, and the list goes on and on. Among this array of choices is “liberal arts education.” Looking over a truly liberal arts education, we might be struck to see the lack of similarity among the classes. We find classes in literature, philosophy, history, mathematics, speech, possibly theology, and the sciences. What exactly is the point of all this? Why would anyone pursue this kind of education? A liberal arts education will not train us to be bricklayers, it will not make us into doctors or lawyers, and it will not enable us to buy a home. It seems entirely gratuitous—something a rich person might indulge in until forced (if ever) to get a “real job.”

First, what exactly is meant by a “liberal arts education”? Many programs today which call themselves “liberal arts” would be unrecognizable as such fifty or more years ago. Today, many “liberal arts” programs have been reduced to “general studies” which contain little to no common core and an abundance of elective choices. Instead, a liberal arts education is one which has no electives whatsoever, for to allow the student to choose his own course of study is to turn over the process of education to the one who is in the least position to know what needs to be known: the student. As Mortimer J. Adler points out, “it is the student who is the master under the elective system … the relatively ignorant and incompetent, choose their own road to learning, according to the fickle interests of their immaturity.” In a liberal arts education, all students receive the same education because the end of liberal arts education is the cultivation of the human mind, not the training for a productive career. Since all are human, all require the same education.

It is the end of liberal arts education itself which is the greatest argument for its pursuit. We should pursue the liberal arts because we are human. No one can choose not to be a human being, one can only choose whether or not to be a good one. To become fully what we are means the cultivation of the mind. James V. Schall states that within each of us is a “longing to know … [this is] the very heart of what we are as rational beings.” Most importantly, and yet often least known, is the need and desire to know “ourselves”—who we are, where we come from, where we are going. Liberal arts education aims to reveal the student to themselves. Gregory Thaumaturgus claims that this was one of the highest things that Origen taught his students: “teaching us to be at home with ourselves, and to desire and endeavor to know ourselves, which indeed is the most excellent achievement of philosophy, the thing that is ascribed also to the most prophetic of spirits as the highest argument of wisdom—the precept, Know thyself.” This indeed is the beginning of knowledge. For without knowledge of ourselves, no amount of our struggling will bring us closer to what we truly need.

So no, the liberal arts will not help you get a bigger boat, a better job, or a beautiful spouse. It will, however, teach you why none of those things, in themselves, will make you happy. Instead, the liberal arts will enable you (no matter what possessions you have, no matter what career you choose, no matter whether you are married or single) to be more human, more of what you were intended to be, and consequently, happier.

Gregory Thaumaturgus. “Oration and Panegyric Addressed to Origen.” In The Great Tradition: Classic Readings on What It Means to Be an Educated Human Being, edited by Richard M. Gamble, 179-80. Wilmington, DE: ISI Books, 2009.

…according to Mortimer J. Adler that is, if that college wants to succeed in meeting the goals of a liberal education:

A liberal arts college should not allow any form of special training for specific jobs, vocations, or even learned professions to intrude itself into the curriculum.

A liberal arts college should not provide any elective courses in its curriculum, nor should it afford any opportunities for specialization in particular subject matters.

The faculty of a liberal arts college should not be divided into departmental groups, each representing special competence in some particular subject matter, and narrow interest in some limited field of learning.

No textbooks should be used in a liberal arts college; there should be no lectures in courses; and formal lectures should be kept to the minimum and should, wherever possible, be of such generality that they can be given to the whole student body.

Written examinations, especially of the objective or true-false type, should be eliminated in favor of oral examinations.

To find out why Adler argues for these five recommendations, see his essay, “Liberal Schooling in the Twentieth Century” (1962).